Answer:
i need more details
Step-by-step explanation:
Answer: 20.57142857
Step-by-step explanation:
148 = 3x + 3 + 4x + 1
Step one: combine like terms
148 = 7x + 4
Step 2: Subtract the 4 over to 148
144 = 7x
Step 3: Divide 7 on both sides
20.57142857 = x
Answer:
Step-by-step explanation:
i think you multiple the 10 and the 12
Answer:
Step-by-step explanation:
Since the second equation is fully simplified and we know what x equals, we plug the entire equation of x in for x in the top equation:
Now solve for y.
Now plug y back into the bottom equation and solve for x.
Answer:
Step-by-step explanation:
Let the length of one side of the square base be x
Let the height of the box by y
Volume of the box V = x²y
Since the box is opened at the top, the total surface area S = x² + 2xy + 2xy
S = x² + 4xy
Given
S = 7500sq in.
Substitute into the formula for calculating the total surface area
7500 = x² + 4xy
Make y the subject of the formula;
7500 - x² = 4xy
y = (7500-x²)/4x
Since V = x²y
V = x² (7500-x²)/4x
V = x(7500-x²)/4
V = 1/4(7500x-x³)
For us to maximize the volume, then dV/dx = 0
dV/dx = 1/4(7500-3x²)
1/4(7500-3x²) = 0
(7500-3x²) = 0
7500 = 3x²
x² = 7500/3
x² = 2500
x = √2500
x = 50in
Since y = (7500-x²)/4x
y = 7500-2500/4(50)
y = 5000/200
y = 25in
Hence the dimensions of the box that will maximize its volume is 50in by 50in by 25in.
The Volume of the box V = 50²*25
V = 2500*25
V= 62,500in³
Hence the maximum volume is 62,500in³